$ KLJK VWHS±XS '&±'& FRQYHUWHU ZLWK 0337 IRU 39 DSSOLFDWLRQ
0DUÕD GHO 5RVDULR 5LYHUD(VSLQRVD∗ $OIUHGR < $OHMDQGUH/RSH]∗ -HVXV ( 3HGUD]D%DUURQ∗ 3HGUR 0DUWÕQ *DUFÕD9LWH∗ DQG +HFWRU 5 5REOHV&DPSRV†
∗7(&10 ,QVWLWXWR 7HFQRORJLFR GH &LXGDG 0DGHUR
'LYLVLRQ GH (VWXGLRV GH 3RVJUDGR H ,QYHVWLJDFLRQ - 5RVDV \ - 8UXHWD VQ /RV 0DQJRV &3 &G 0DGHUR 7DPV 0H[LFR WHO
†8QLYHUVLGDG 3DQDPHULFDQD &DPSXV *XDGDODMDUD )DFXOWDG GH ,QJHQLHUÕD =DSRSDQ -DOLVFR &3 0H[LFR
$EVWUDFW²7KLV SDSHU H[KLELWV WKH SHUIRUPDQFH RI D KLJK VWHS±
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
, ,1752'8&7,21
$ SKRWRYROWDLF 39 SDQHO KDV D XQLTXH RSHUDWLQJ SRLQW FDOOHG WKH 0D[LPXP 3RZHU 3RLQW 033 DW ZKLFK WKH H[WUDF WLRQ RI WKH DYDLODEOH SRZHU LV PD[LPL]HG IRU JLYHQ FOLPDWLF FRQGLWLRQV VXFK DV WHPSHUDWXUH DQG VRODU UDGLDWLRQ >@
7KH 033 GHSHQGV QRW RQO\ RQ WKH FOLPDWLF FRQGLWLRQV EXW DOVR RQ WKH 39 SDQHO PDQXIDFWXULQJ FKDUDFWHULVWLFV WKDW PHDQV HYHU\ PRGXOH PLJKW KDYH D GLIIHUHQW 033 HYHQ LQ FHOOV RI WKH VDPH W\SH %HVLGHV WKLV 033 PRYHV LQ DQ XQSUHGLFWDEOH ZD\
(YHQ WKRXJK LW LV SRVVLEOH WR REWDLQ WKH FXUUHQWYROWDJH RU ,9 FXUYH RI WKH 39 SDQHO E\ PHDQV RI H[SHULPHQWDO PHDVXUHPHQWV LQ RUGHU WR NQRZ WKH 033 ORFDWLRQ LW LV QHFHVVDU\ WR XVH HI¿FLHQW WHFKQLTXHV IRU WUDFNLQJ WKH 033 >@ $OJRULWKPV IRU H[WUDFWLQJ WKH PD[LPXP SRZHU IURP WKH 39 SDQHO DUH FDOOHG 033 WUDFNHUV 0337 7KXV PDQ\ 0337 DOJRULWKPV KDYH EHHQ GHYHORSHG LQ RUGHU WR DFKLHYH PD[LPXP HI¿FLHQF\ LQ RSHUDWLRQ >@ >@
7KH 39 SDQHO FXUYH FDQ EH H[SHULPHQWDOO\ REWDLQHG HP SOR\LQJ GLIIHUHQW PHWKRGV RQH RI WKH VLPSOHVW FRQVLVWV LQ FRQQHFWLQJ D YDULDEOH UHVLVWRU DW WKH PRGXOH WHUPLQDOV 7KHQ YDOXHV RI FXUUHQW DQG YROWDJH DUH UHJLVWHUHG IRU GLIIHUHQW ORDG FRQGLWLRQV DQG ¿QDOO\ WKH GHOLYHUHG SRZHU LV FRPSXWHG >@
.QRZLQJ WKH H[DFW ORFDWLRQ RI WKH 033 DOORZV WKH LPSOHPHQ WDWLRQ RI VWUDLJKWIRUZDUG DOJRULWKPV EDVHG RQ WKH LUUDGLDQFH YDOXH KRZHYHU DQ H[WUD VHQVRU LV UHTXLUHG ZKLFK LQFUHDVHV WKH WRWDO FRVW
)LJ FRQWDLQV D W\SLFDO FRQ¿JXUDWLRQ RI D 39 V\VWHP ZKLFK LV FRQVWLWXWHG E\ D SRZHU FRQYHUWHU FRQWUROOHG E\ DQ 0337 DOJRULWKP IHHGLQJ D ¿[HG '& ORDGRL 7KH '&−'& FRQYHUWHU ZLWK D YROWDJH JDLQ RI Gv FDQ HPXODWH D YDULDEOH UHVLVWDQFH
MRLQLQJ WKH 39 PRGXOH DQG WKH ORDG ,Q WHUPV RI DYHUDJH YDOXHV WKH FRQYHUWHU EHKDYHV DV DQ LPSHGDQFH ZKLFK GHSHQGV RQ WKH YDOXH RIRL DQG GXW\ F\FOH ' >@ ,Q RUGHU WR RSHUDWH DW WKH 033 WKH GXW\ F\FOH JHQHUDWHG E\ WKH 0337 DOJRULWKP QHHGV WR EH DGMXVWHG LW LV HVVHQWLDO WR VHOHFW D VXLWDEOH FRQYHUWHU WKDW DOORZV UHDFKLQJ WKH 033 IRU D VSHFL¿FRL DQG WKHUHIRUH WKH FRQYHUWHU LQSXW LPSHGDQFH VHHQ E\ WKH PRGXOHZin
%DVLF FRQYHUWHU WRSRORJLHV VXFK DV EXFN DQG ERRVW DUH ZLGHO\ XVHG IRU 0337 DSSOLFDWLRQV EHFDXVH RI WKHLU VLPSOLFLW\
1HYHUWKHOHVV WKHUH LV D KXJH QXPEHU RI SRZHU FRQYHUWHUV ZHOO UHSRUWHG LQ WKH OLWHUDWXUH >@ WKDW HQMR\ WKHLU RZQ DGYDQWDJHV
$Q DSSURSULDWH '&−'& FRQYHUWHU VHOHFWLRQ ZLOO JXDUDQWHH UHDFKLQJ DOO WKH UDQJH RI RSWLPDO LPSHGDQFH YDOXHV WKDW WKH V\VWHP UHTXLUHV WKURXJKRXW WKH VXQ KRXUV 2Q WKH RQH KDQG IRU ORZ LUUDGLDQFH FRQGLWLRQV D KLJK JDLQ LV GHVLUHG LQ RUGHU WR FRPSO\ WKH ORDG YROWDJH OHYHO WKXV VHYHUDO KLJK JDLQ FRQYHUWHUV KDYH EHHQ SURSRVHG KRZHYHU WKH\ XVXDOO\ SUHVHQW FRPSOH[
FRQ¿JXUDWLRQ DQG PRUH WKDQ RQH VLQJOH SRZHU WUDQVLVWRU ZKLFK LQ WXUQ LQFUHDVHV WKH ORVVHV ZKHUHDV RWKHUV DUH UHDOL]HG ZLWK D VLQJOH SRZHU VZLWFK >@ RYHUFRPLQJ WKLV GLVDGYDQWDJH 2Q WKH RWKHU KDQG FRQYHUWHUV ZLWK JDLQ ÀH[LELOLW\ OLNH WKH FRQYHQ WLRQDO EXFN±ERRVW DUH PRUH DGHTXDWH IRU 39 DSSOLFDWLRQV VLQFH WKH\ RIIHU DQ RXWSXW YROWDJH KLJKHU RU ORZHU WKDQ WKH LQSXW YROWDJH >@ +RZHYHU WKH LQSXW FXUUHQW GLVFRQWLQXLW\ GHWHULR UDWHV WKH 0337 DOJRULWKP SHUIRUPDQFH >@ ,W LV GHVLUDEOH WKDW WKH FRQYHUWHU RSHUDWHV RQ WKH &RQWLQXRXV &RQGXFWLRQ 0RGH
&&0 IRU KLJK HI¿FLHQF\ DQG FRQWLQXRXV FXUUHQW WKURXJK WKH LQGXFWRU
Panel PV D
+ +
- -
RLVi Vo
ii io
M P P T Controller Zi DC−DC Converter
G
v)LJ %ORFN GLDJUDP RI WKH 39 SDQHO ZLWK 0337 FRQWURO
F ,(((
7KLV SDSHU VXJJHVWV WKH XWLOL]DWLRQ RI D ERRVW '&−'&
FRQYHUWHU >@ ZLWK GLRGH±FDSDFLWRU PXOWLSOLHU FRQWUROOHG E\
DQ 0337 DOJRULWKP WR LQWHUIDFH D 39 SDQHO ZLWK D ¿[HG ORDG 7KH RSHUDWLRQ SULQFLSOHV DQDO\VLV DQG WKH VLPXODWLRQ UHVXOWV RI WKH SURSRVHG FRQYHUWHU DUH SUHVHQWHG %HVLGHV JXLGHOLQH IRU SRZHU FRQYHUWHU VHOHFWLRQ EDVHG RQ WKH LQSXW LPSHGDQFH FKDUDFWHULVWLFV DUH SURYLGHG DOVR WKH XWLOL]DWLRQ RI D SURSRVHG '&−'& FRQYHUWHU FRQWUROOHG E\ DQ 0337 DOJRULWKP LV VXJ JHVWHG DQG DQDO\]HG $ VWDQGDUG 0337 DOJRULWKP LV WDNHQ DV D UHIHUHQFH LQ RUGHU WR HYDOXDWH WKH SURSRVHG '&±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
,, 0337 7(&+1,48(6
$V PHQWLRQHG EHIRUH WKHUH DUH VHYHUDO 0337 DOJRULWKPV UHSRUWHG LQ WKH OLWHUDWXUH >@ VRPH RI WKHP DUH YHU\ VLPSOH DQG HDV\ WR LPSOHPHQW $OJRULWKPV PRVW IUHTXHQWO\ IRXQG LQ WKH OLWHUDWXUH DUH WKH )UDFWLRQDO 2SHQ &LUFXLW 9ROWDJH >@
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
QXPEHU RI UHTXLUHG VHQVRUV FRQYHUJHQFH VSHHG DQG VWDELOLW\
3DUWLFXODUO\ WKH 3 2 DOJRULWKP VKRZQ LQ )LJ LV HDV\
WR GHVLJQ DQG LPSOHPHQW LW GRHV QRW QHHG WKH 39 SDQHO PRGHO DQG LW FDQ EH LPSOHPHQWHG HLWKHU ZLWK DQDORJ RU GLJLWDO FLUFXLWU\ >@
7KH 3 2 DOJRULWKP RSHUDWHV E\ FKDQJLQJ WKH 39 SDQHO RSHUDWLQJ YROWDJH DQG REVHUYLQJ WKH SRZHU GUDZQ IURP WKH 39 VRXUFH 7KH ÀRZFKDUW RI WKH 3 2 PHWKRG LV SUHVHQWHG LQ )LJ 7KH 0337 DOJRULWKP LV FRQWLQXRXVO\ VDPSOLQJ WKH DFWXDO 39 RXWSXW YROWDJHVkDQG FXUUHQWIk WKHQ WKH SRZHUPk
LV FDOFXODWHG 7KH GLIIHUHQFHV EHWZHHQ WKH SRZHU DQG YROWDJH DUH REWDLQHG LQ dP DQGdV DW WKH LQVWDQWk DQGk−1 )RU D SRVLWLYH YDOXH RI dV LIdP LV SRVLWLYH WKH VWHS SHUWXUEDWLRQ ΔD VKRXOG LQFUHDVH ZKHUHDV LI dP LV QHJDWLYH ΔD PXVW GHFUHDVH 2Q WKH RWKHU KDQG IRU D QHJDWLYH YDOXH RIdVΔD
VKRXOG FKDQJH LQ DQ RSSRVLWH ZD\ DV LQGLFDWHG LQ )LJ >@
$IWHU D VHYHUDO QXPEHU RI LWHUDWLRQ VWHSV WKH 3 2 DOJRULWKP ZLOO PDNH WKH RSHUDWLQJ SRLQW RVFLOODWH DURXQG WKH 033
,,, &219(57(57232/2*,(6
7KH HTXLYDOHQW LQSXW LPSHGDQFH Zin RI D SRZHU FRQYHUWHU WDNHV UHOHYDQW LPSRUWDQFH LQ 39 SDQHO DSSOLFDWLRQV VLQFH WKH
dP >0 Y N
Y N
Start
Pk=Vk·Ik
dP =Pk−Pk−1
dV =Vk−Vk−1
dV >0 Y dV >0
N
MeasureVkandIk
D=D−ΔD
D=D+ ΔD D=D−ΔD D=D+ ΔD
)LJ )ORZFKDUW RI 3 2 DOJRULWKP
XOWLPDWH REMHFWLYH RI WKH FRQYHUWHU LV WR PDQLSXODWH WKH ORDG
³VHHQ´ E\ WKH VRXUFH ,Q VKRUW WKH FRQYHUWHU DFWV DV DQ LQWHUIDFH EHWZHHQ WKH ORDG UHVLVWRU ZKLFK FRQVXPHV XVHIXOO\ WKH HQHUJ\
DQG WKH 39 SDQHO 7DEOH , VXPPDUL]HV LGHDO YROWDJHV DQG FXUUHQWV UHODWLRQVKLSV RI FRQYHQWLRQDO SRZHU FRQYHUWHUV DORQJ ZLWK WKH SURSRVHG KLJK VWHS±XS SRZHU FRQYHUWHU 7KH LQSXW FKDUDFWHULVWLF Zin RI HDFK FRQYHUWHU LV DOVR SURYLGHG 7KH ORDG YDOXHRL GHSHQGV RQ WKH SDUWLFXODU DSSOLFDWLRQ KRZHYHU WKH HTXLYDOHQW LPSHGDQFH FDQ EH PRGL¿HG SURSHUO\ E\ WKH SRZHU FRQYHUWHU WKXV FRPSRQHQWV VHOHFWLRQ LV YHU\ LPSRUWDQW LQ WKH GHVLJQ SURFHVV 0RUHRYHU LW LV ZRUWK QRWLQJ WKDW RL
GHWHUPLQHV WKH UDQJH RIZin QHHGHG WR DFKLHYH WKH 033 DQG WKH UDQJH RI GXW\ F\FOHV LQ ZKLFK WKH FRQYHUWHU ZLOO RSHUDWH
7$%/( , &RQYHUWHU SDUDPHWHUV 3DUDPHWHU
&RQYHUWHU VVo
i
Io
Ii Zin
EXFN D D1 RDL2
ERRVW 1−D1 1−D (1−D)2RL
EXFN±ERRVW 1−D−D 1−D (1−D)D2 2RL
+LJK VWHS±XS 1+D1−D 1−D1+D (1−D)(1+D)22RL
)RU D FHUWDLQ ORDG WKH 39 SDQHO ³VHHV´ DQ LQSXW LPSHGDQFH DV SORWWHG LQ WKH )LJ $QG WKH PRVW UHPDUNDEOH FKDUDFWHU LVWLFV DUH WKH IROORZLQJ L FRQYHUWHUV ZLWK ERRVW FDSDELOLW\
KDYH D Zin < RL FRQGLWLRQ LL IRU WKH EXFN FRQYHUWHU WKH FKDUDFWHULVWLF LV WKDW Zin > RL DQG LLL WKH EXFN±ERRVW FRQYHUWHUV FDQ KDYH DQ LQSXW LPSHGDQFH LQ D ZLGHU UDQJH LQFOXGLQJ ORZHU RU JUHDWHU YDOXHV RIRL
,W LV LPSRUWDQW WR QRWH WKDWZinGHFUHDVHV ZKLOH WKH YDOXH RI ' ULVHV DV )LJ VKRZV
7KH DGYDQWDJH RI XVLQJ WKH KLJK VWHS±XS FRQYHUWHU LV WKDW WKH
1RUPDOL]HG= LQ
'XW\&\FOH
%XFN
%XFN%RRVW
%RRVW 3URSRVHG%RRVW
)LJ (TXLYDOHQW LQSXW LPSHGDQFH RI YDULRXV SRZHU FRQYHUWHUV 39 SDQHO LV DOZD\V ORDGHG ZLWK D ORZHU LPSHGDQFH LQ VSLWH RI SRVVHVVLQJ KLJK YROWDJH JDLQ $V D UHVXOW WKH PD[LPXP H[WUDFWHG SRZHU FDQ EH DFKLHYHG ZLWK D UHODWLYHO\ ORZ GXW\
F\FOH ZKLFK LV GHVLUDEOH JLYHQ WKH IDFW WKDW LW NHHSV WKH ORVVHV ORZ
,9 $33/,&$7,216 2) 7+(0337$/*25,7+0 7ZR GLIIHUHQW UHDOL]DWLRQV RI WKH 0337 DOJRULWKP IRU 39 V\VWHPV FDQ EH DFFRPSOLVKHG 7KH XWLOL]DWLRQ RI D '&$&
FRQYHUWHU LQ RUGHU WR WUDQVIRUP WKH '& SRZHU IURP WKH 39 PRGXOH WR $& SRZHU LV XVHG LQ V\VWHPV FRQQHFWHG WR WKH XWLOLW\ JULG +RZHYHU WKLV VWXG\ LV QRW FRQVLGHUHG LQ WKLV ZRUN 6WDQG±DORQH 39 V\VWHPV DUH FRPPRQO\ XVHG LQ ORZ±SRZHU DSSOLFDWLRQV $Q HQHUJ\ VWRUDJH GHYLFH VXFK DV D EDWWHU\ LV QHFHVVDU\ 7KH VLPSOHVW ZD\ RI LQWHJUDWLQJ D EDWWHU\ ZLWK D 39 SDQHO LV WKH GLUHFW SDUDOOHO FRQQHFWLRQ 1HYHUWKHOHVV WKH EDWWHU\ WHQGV WR FRQWURO WKH 39 YROWDJH DQG GRHV QRW DOORZ RSHUDWLQJ LQ WKH 033 0RUHRYHU WKLV FRQGLWLRQ UHGXFHV WKH HI¿FLHQF\ RI WKH V\VWHP DQG LW LV QRW SRVVLEOH WR UHJXODWH WKH EDWWHU\ SRZHU >@ )RU WKDW UHDVRQ LW LV QHFHVVDU\ WR FRQQHFW D '&±'& FRQYHUWHU EHWZHHQ WKH 39 SDQHO DQG WKH EDWWHU\
%DWWHU\ FKDUJHU V\VWHPV DUH ZLGHO\ XVHG LQ VWDQG±DORQH 39 V\VWHPV DV SUHVHQWHG LQ >@ ZLWK D QRYHO EDWWHU\ FKDUJLQJ UHJXODWLRQ V\VWHP ,W FRQVLVWV RI D EXFN FRQYHUWHU FRQWUROOHG E\ DQ 0337 WHFKQLTXH 7KH LQFUHDVH RI WKH EDWWHU\ OLIHWLPH DQG WKH EHWWHU H[SORLWDWLRQ RI WKH 39 VRXUFH DUH WKH DGYDQWDJHV RI WKLV PHWKRG 6LPLODUO\ LQ >@ DQ 0337 DOJRULWKP EDVHG RQ D YROWDJH VHQVRU IRU D 6(3,& FRQYHUWHU ZLWK D EDWWHU\ ORDG LV LPSOHPHQWHG
9 $1$/<6,6 2) 352326(' 7232/2*<
7KH =±VRXUFH ZDV ¿UVW LQWURGXFHG IRU RYHUFRPLQJ WKH OLPLWHG YROWDJH JDLQ LQ '&±$& SRZHU FRQYHUVLRQ >@ 7KH
=±VRXUFH DOORZV LQFUHDVLQJ WKH RXWSXW YROWDJH E\ VWRULQJ WKH HQHUJ\ LQ DQ /& ¿OWHU WKHQ GHOLYHULQJ LW IHHGLQJ WKH FRQYHQWLRQDO FRQYHUWHU ZLWK D YROWDJH ODUJHU WKDQ WKH LQSXW YROWDJH $QRWKHU DSSURDFK IRU LQFUHDVLQJ WKH JDLQ FRQVLVWV LQ HPSOR\LQJ GLRGH±FDSDFLWRU SDLUV IRU PXOWLSO\LQJ WKH RXWSXW YROWDJH LQ D '&−'& FRQYHUWHU %RWK WRSRORJLHV DUH DUUDQJHG LQ D IXOOEULGJH FRQ¿JXUDWLRQ EXW WKH ODWWHU LGHD LV WDNHQ IRU UHDOL]LQJ D IDPLO\ RI FRQYHUWHU >@ 7KH SURSRVHG FRQYHUWHU IRU 033 DSSOLFDWLRQV LV VKRZQ LQ )LJ
7KH SURSRVHG FRQYHUWHU LV FRQVWLWXWHG E\ WKH FRPELQDWLRQ RI D FRQYHQWLRQDO ERRVW FRQYHUWHU ZLWK D GLRGHFDSDFLWRU PXO WLSOLHU IRU REWDLQLQJ DQ DGGLWLRQDO JDLQ EHVLGHV DQ /& ¿OWHU IRU
v
d− +
v
o S1+
−
Cp
L1
i
L1Dn
R − +
Boost Converter
Dp
Cn
− +
Multiplier cell
Co
i
Lo− +
Lo
LC filter Common
parts
)LJ 3URSRVHG WRSRORJ\
VPRRWKLQJ WKH RXWSXW YROWDJH SURGXFHG E\ WKH 033 DOJRULWKP DQG WKH VZLWFKLQJ SURFHVV 'LIIHUHQW SDUWV DUH LGHQWL¿HG LQ )LJ LW LV ZRUWK QRWLQJ WKDW DP DQG Cn DUH VKDUHG E\
WKH ERRVW FRQYHUWHU DQG WKH PXOWLSOLHU SDUWV )RU WKH IROORZLQJ DQDO\VLV WKH HTXLYDOHQW VHULHV UHVLVWDQFHV RI WKH LQGXFWRUV LV DOVR WDNHQ LQWR DFFRXQW UHSUHVHQWHG E\ rL(1,o) IRU REWDLQLQJ D PRUH UHDOLVWLF EHKDYLRXU
$ (TXLYDOHQW FLUFXLW VWDWHV
6LQFH WKH SURSRVHG WRSRORJ\ FRQWDLQV RQO\ RQH VLQJOH SRZHU VZLWFK WZR HTXLYDOHQW FLUFXLWV DUH REWDLQHG VHHQ LQ )LJ 1HYHUWKHOHVV LW LV DOZD\V H[SHFWHG WR ZRUN LQ WKH &&0
v
d +−
Cn
Cp
L1
i
L1 Co R− +
i
Lo− + rL1
v
o− + Lo rLo
− +
i
Coi
CpD (TXLYDOHQW FLUFXLW FRUUHVSRQGLQJ WR WKH DFWLYH VWDWH
v
dv
o+
−
Cn
L1
i
L1− R rL1
− +
Lo rLo
Cp
−
+ Co
−
+ +
i
Loi
Coi
Cni
CpE (TXLYDOHQW FLUFXLWV FRUUHVSRQGLQJ WR WKH LQDFWLYH VWDWH )LJ (TXLYDOHQW FLUFXLWV IRU WKH SURSRVHG FRQYHUWHU
$FWLYH VWDWH 0 ≤ t ≤ DTs )RU WKLV VWDWH ZLWK WKH FRPPDQGLQJ VLJQDOq(t) = 1 WKH LQSXW LQGXFWRU LV FRQQHFWHG GLUHFWO\ WR WKH LQSXW YROWDJH SURGXFLQJ DQ LQFUHDVLQJ LQ LWV FXUUHQW DV LQGLFDWHV 'XH WR Cn EHORQJV WR WKH ERRVW FRQYHUWHU VWDJH LWV YROWDJH LV FORVH WRvd/(1−D)9 7KH /&
¿OWHU LV IHG E\ WKH VHULHV FRQQHFWLRQ RICpDQGCn SURYLGLQJ 2·vd/(1−D)9 7KHUHIRUH WKH RXWSXW VWDJH FDQ EH VHHQ DV D EXFN FRQYHUWHU ZKRVH LQSXW YROWDJH LV WZLFHvd/(1−D)9 DV LOOXVWUDWHG LQ )LJ D 'XULQJ WKLV VWDWH ERWK GLRGHV DUH UHYHUVH ELDVHG EORFNLQJ WKHLU FRUUHVSRQGLQJ FDSDFLWRU YROWDJHV
VL1 =L1ΔiL1
Δt =L1ΔiL1
DT s =Vd−iL1rL1 ,QDFWLYH VWDWH DTs < t ≤ (1−D)Ts )RU WKLV VWDWH ZLWK WKH FRPPDQGLQJ VLJQDOq(t) = 0 WKH HTXLYDOHQW FLUFXLW LV SUHVHQWHG LQ )LJ E 'XULQJ WKLV VWDWH WKH SRZHU WUDQVLVWRU LV WXUQHG RII ZKHUHDV ERWK GLRGHV DUH IRUZDUGELDVHG FRQQHFWLQJ FDSDFLWRUVCn \Cp LQ SDUDOOHO $V D FRQVHTXHQFH WKH RXWSXW
¿OWHU LV IHG ZLWK vd/(1−D)9 &XUUHQW WKURXJKL1 GHFUHDVHV ZLWK D UDWH JLYHQ E\
VL1 =L1 ΔiL1
(1−D)T s =Vd−iL1rL1−VCn
% 2XWSXW YROWDJH RI WKH SURSRVHG FRQYHUWHU
$V FXVWRPDU\ LQ SRZHU HOHFWURQLFV FRQYHUWHU D ORVVOHVV DQDO\VLV LV FDUULHG RXW $YHUDJLQJ WKH LQGXFWRU YROWDJH GXULQJ D VZLWFKLQJ SHULRG DQG WDNLQJ LQWR DFFRXQW WKH FXUUHQW LQFUHPHQW ΔiL WKH LQSXWRXWSXW UHODWLRQVKLS FDQ EH REWDLQHG
ΔiL(1,o)
q=0+ ΔiL(1,o)
q=1= 0
:LWK WKH XVH RI DQG WKH WRWDO YROWDJH JDLQ LV VCo
Vd =VC
Vd·VCo
VC = (1 +D)
(1−D)· 1 1 + (1+D)(1−D)22rL1
· 1 1 +rL0
& 2XWSXW YROWDJH RI WKH EXFN PRGHO
%RWK VWDWHV FDQ EH FRPELQHG LQ WKH PRGHO VKRZQ LQ )LJ ZKLFK UHVHPEOHV D %XFN FRQYHUWHU ZKRVH LQGXFWRU VZLWFKHV EHWZHHQ vd DQG 2vd LQ WKLV ZD\ WKH DYHUDJH RXWSXW YROWDJH FDQ EH HDVLO\ FRPSXWHG
2vd
Co R
q= 0
− vd +
q= 1
Lo
)LJ %XFN PRGHO
$V DVVXPHG LQ )LJ WKH DYHUDJH YROWDJH DW WKH ORDG VLGH FRUUHVSRQGV WR ZLWK WKH SDUDVLWLF HOHPHQW RI LQGXFWRUV VHW WR ]HUR
9, 32:(5 &219(57(5 :,7+0337&21752//(5
7KH PDLQ REMHFWLYH RI WKH 0337 LV WR PDWFK UDSLGO\ WKH LPSHGDQFH Zin ZLWK WKH RSWLPDO LPSHGDQFH RI 39 PRGXOH DW WKH 033 7KH SHUWXUEDWLRQ VWHS VL]H DQG WKH SHUWXUEDWLRQ WLPH DUH WZR GHFLVLYH IDFWRUV 7KH RXWSXW SRZHU RVFLOODWLRQ
PDJQLWXGH GHSHQGV GLUHFWO\ RQ WKH VWHS VL]H WKH VPDOOHU VWHS XVHG LV WKH ORZHU ULSSOH REWDLQHG ZKLFK LV GHVLUDEOH DQG LW JLYHV PRUH VHQVLWLYHQHVV WR WKH DOJRULWKP 7KH SHUWXUEDWLRQ WLPH LV DOVR FUXFLDO VLQFH LW FRQWUROV WKH 0337 UHVSRQVH WLPH EHLQJ DEOH WR WUDFN WKH 033 VXFFHVVIXOO\ HYHQ ZLWK WHPSHUDWXUH DQG LUUDGLDQFH YDULDWLRQV >@
7R VHOHFW WKH YDOXH RI R WKH VLPXODWLRQ RI WKH 39 PRGXOH ZLWKRXW WKH 0337 FRQWUROOHU ZDV DQDO\]HG XQGHU FRQVWDQW LUUDGLDQFH DQG WHPSHUDWXUH
G= 1,000:/P2, T = 25◦C 7KHQ XVLQJ WKH YROWDJH DQG FXUUHQW DW 033 Vm, Im GHSLFWHG LQ )LJ 7KXV WKH YDOXH RI Rm ZDV FDOFXODWHG IURP E\
2KP¶V ODZ
Current(A)
Voltage (V)
Power(W)
033
9PD[,PD[
,SY 3SY
)LJ 39 FXUYH VROLG ,9 FXUYH GDVKHG Rm= Vm
Im
)RU PD[LPXP SRZHU WUDQVIHURm PXVW EH HTXDO WRR
9,, 6,08/$7,21 5(68/76
,Q RUGHU WR YDOLGDWH WKH SURSRVHG V\VWHP D 0DWODE 6LPXOLQN VLPXODWLRQ ZLWK WKH SDUDPHWHUV JLYHQ LQ WKH $SSHQGL[ ZDV UXQ 7KH FORVHG ORRS V\VWHP LV VKRZQ LQ )LJ ZKLFK LQFRUSR UDWHV WKH FODVVLFDO 3 2 DOJRULWKP ZLWK WKH SRZHU FRQYHUWHU ,Q RUGHU IRU WKH 0337 FRQWUROOHU WR FDOFXODWH WKH SRZHU SURYLGHG E\ WKH 39 SDQHO YROWDJH DQG FXUUHQW VHQVRUV ZHUH HPSOR\HG WR PHDVXUH VXFK YDULDEOHV
DC-DC Converter
P&O Algorithm i
mv
pvD v
mi
pvi
o+
−
+
V
−oR
LPV
)LJ &ORVHG /RRS V\VWHP
7KH 6RODUH[ 06;− >@ ZDV VHOHFWHG DV WKH 39 SDQHO PRGHO IRU WKH VLPXODWLRQ 7KH PRGXOH FRQVLVWV RI SRO\
FU\VWDOOLQH VLOLFRQ VRODU FHOOV HOHFWULFDOO\ FRQ¿JXUHG DV WZR VHULHV VWULQJV RI FHOOV HDFK DQG SURYLGHV : DV QRPLQDO PD[LPXP SRZHU LQ 67& 7KH VLPXODWLRQ PRGHO ZDV EDVHG RQ WKH RQH SUHVHQWHG LQ >@
$ FRPSDULVRQ EHWZHHQ WKH SURSRVHG WRSRORJ\ DQG WKH FRQYHQWLRQDO ERRVW FRQYHUWHU LV SUHVHQWHG 7KH VZLWFKLQJ IUH TXHQF\ WKDW FRQWUROV WKH SURSRVHG FRQYHUWHU ZDV VHW DW N+] WKH 39 V\VWHP ZDV SHUWXUEHG SHULRGLFDOO\ HYHU\
PV ZLWK D GXW\ F\FOH FKDQJH ΔD RI± 7KH V\VWHP ZDV HYDOXDWHG E\ DSSO\LQJ D VWHS FKDQJH LQ WKH LUUDGLDQFH IURP :P2WR :P2ZLWK D FRQVWDQW PRGXOH WHPSHUDWXUH 7 RI ◦& 5HVXOWV RI WKH VLPXODWLRQ DUH VKRZQ LQ )LJ
$V VKRZQ LQ )LJ D DQG )LJ E WKH FRQYHUWHUV DUH FDSDEOH RI WUDFNLQJ WKH 033 LUUHVSHFWLYH RI LQFUHDVH RU GHFUHDVH LQ LUUDGLDQFH 7KH 39 SRZHU SUHVHQWV VPDOO RVFLOODWLRQV GXH WR WKH LQKHUHQW FKDUDFWHULVWLFV RI WKH 3 2 DOJRULWKP 0RUH VRSKLVWLFDWHG DOJRULWKPV PD\ EH LPSOHPHQWHG ZLWK D EHWWHU SHUIRUPDQFH KRZHYHU WKH\ DUH RXW RI WKH VFRSH RI WKLV ZRUN )RU SUDFWLFDO SXUSRVHV LW LV FRQVLGHUHG D ORZ ULSSOH DQG KDV QR XQGHVLUDEOH HIIHFWV RQ WKH SRZHU TXDOLW\
3RZHU:
WLPHPV
3URSRVHG
%RRVW
D 0D[LPXP SRZHU H[WUDFWHG XQGHU LUUDGLDWLRQ YDULDWLRQV
3RZHU:
WLPHPV
3URSRVHG
%RRVW
E 0D[LPXP SRZHU H[WUDFWHG ]RRPHGLQ )LJ 6LPXODWLRQ SHUIRUPDQFH RI WKH SURSRVHG V\VWHP )LJ VKRZV WKH HYROXWLRQ RI WKH GXW\ F\FOHV RI ERWK FRQYHUWHUV XQGHU WKH VDPH GLVWXUEDQFH DQG 3 2 DOJRULWKP SDUDPHWHU FRQGLWLRQV $V FDQ EH VHHQ WKH GXW\ F\FOH GHWHU PLQHG E\ WKH 0337 RSHUDWLQJ ZLWK WKH SURSRVHG FRQYHUWHU LV VLJQL¿FDQWO\ VPDOOHU WKDQ WKDW RI WKH ERRVW FRQYHUWHU )LJ VKRZV WKH SRZHU H[WUDFWHG YHUVXV WKH 39 YROWDJH DFFRUGLQJ WR WKH DOJRULWKP ZKHQ D VWHS FKDQJH LQ WKH LUUDGLDQFH RFFXUV LQ ERWK FRQYHUWHUV ,W FDQ EH REVHUYHG WKDW WKH RSHUDWLQJ SRLQW SDWK DFKLHYHV WKH PD[LPXP YDOXH HYHQ ZKHQ D UDSLG FKDQJH LQ LUUDGLDQFH RFFXUV
9,,, (;3(5,0(17$/ 5(68/76
,Q WKLV VHFWLRQ LV SUHVHQWHG WKH EHKDYLRXU RI WKH RXWSXW 39 SRZHU E\ PDQLSXODWLQJ WKH YDOXH RI Zin )LJ VKRZV WKH ODERUDWRU\ SURWRW\SH XVHG IRU WKLV H[SHULPHQW $ FRQYHQWLRQDO ERRVW FRQYHUWHU ZDV LPSOHPHQWHG IRU WKLV VWXG\ DQG WKHLU
'XW\&\FOH
WLPHPV
3URSRVHG
%RRVW
)LJ 6LPXODWHG ZDYHIRUPV 'XW\ &\FOHV DW 033
39YROWDJH9
3RZHU:
3URSRVHG
%RRVW
)LJ 3RZHU DQG YROWDJH 39 IRU ERWK FRQYHUWHUV FRPSRQHQWV DUH OLVWHG LQ 7DEOH ,, $ VZLWFKLQJ IUHTXHQF\
VLJQDO RI N+] ZLWK D YDULDEOH GXW\ F\FOH IURP WR ZDV DSSOLHG WR WKH SRZHU FRQYHUWHU $GGLWLRQDOO\ WKHVpv
DQGipvSURGXFHG E\ D SRO\FU\VWDOOLQH JHQHULF 39 SDQHO ZHUH PHDVXUHG ZLWK FXUUHQW DQG YROWDJH VHQVRUV E\ PHDQV WKH $'&
RI $7PHJD3 PLFURFRQWUROOHU 7KHVH VLJQDOV ZHUH FDSWXUHG ZLWK D GLJLWDO VFRSH 736 IURP 7HNWURQL[
)LJ 3URWRW\SH SKRWR
)LJ SUHVHQWV WKH GXW\ F\FOHV FRUUHVSRQGLQJ WR WKH PD[LPXP SRZHU JHQHUDWHG E\ WKH 39 SDQHO $V SUHVHQWHG LQ 7DEOH , LW LV HYLGHQW WKDW WKHUH LV D FRUUHVSRQGLQJ YDOXH RI ' IRU D GLIIHUHQWRL DW ZKLFK WKH RXWSXW SRZHU UHDFKHV WKH PD[LPXP SRLQW %\ FKDQJLQJRLWR D KLJKHU YDOXH WKH VXLWDEOH ' REWDLQHG H[SHULPHQWDOO\ LQFUHDVHV VR WKDW WKH YDOXH RI Zin
EHFRPHV VPDOOHU RWKHUZLVHZin JHWV KLJKHU ,; &21&/86,216
,Q WKLV SDSHU D KLJK VWHS−XS '&−'& FRQYHUWHU VXLWDEOH IRU 39 DSSOLFDWLRQV ZDV SURSRVHG 7KLV FRQYHUWHU SUHVHQWV D KLJKHU YROWDJH JDLQ WKDQ WKDW RI D FRQYHQWLRQDO ERRVW FRQYHUWHU DQG LW LV DSSURSULDWH IRU WKLV SXUSRVH $ VLPXODWLRQ LQFOXGLQJ D 3 2 0337 WHFKQLTXH ZDV VKRZQ WR VXSSRUW LWV HIIHFWLYHQHVV HYHQ XQGHU YDU\LQJ LUUDGLDQFH 7KLV SDSHU H[SODLQV WKH RSHUDWLQJ SULQFLSOH RI WKH SURSRVHG FRQYHUWHU 8QOLNH WKH FRQYHQWLRQDO
/RJLF
7LPHPVGLY
5/ :
/RJLF
7LPHPVGLY
/RJLF
5/ :
5/ :
)LJ ([SHULPHQWDO ZDYHIRUPV 'XW\ &\FOHV DW 033 ERRVW FRQYHUWHU WKH VXJJHVWHG WRSRORJ\ FDQ H[WUDFW WKH PD[L PXP SRZHU ZLWK D UHODWLYHO\ ORZ GXW\ F\FOH 7KH H[SHULPHQWDO UHVXOWV HYLGHQFH WKH HIIHFW RI WKH LQSXW LPSHGDQFH LQ WKH FORVHG ORRS V\VWHP DQG VKRZ WKH YDOXHV RI GXW\ F\FOH WKDW WKH 0337 PXVW SURYLGH IRU JLYHQ FRQGLWLRQV
$&.12:/('*0(17
7KH DXWKRUV ZRXOG OLNH WR WKDQN 7(&12/ 2*,&2 1$
&,21$/ '( 0 (;,&2 DQG ,QVWLWXWR 7HFQRORJLFR GH &LXGDG 0DGHUR IRU VXSSRUWLQJ WKLV UHVHDUFK XQGHU *UDQW −3
$33(1',;
7$%/( ,, 3DUDPHWHUV RI WKH YDULRXV FRPSRQHQWV 6\PERO 9DOXH
3RZHU &RPSRQHQWV
%RRVW &RQYHUWHU vin 9 L1 μ+ Cn μ)
R Ω ΩDQG Ω 3URSRVHG 7RSRORJ\
vin 9 L1=Lo μ+
Cp=Cn=Co μ)
R Ω
'HYLFHV 0&8 $7PHJD3
S1 )''
D1 1*
*DWH GULYHU $ 5()(5(1&(6
>@ 1 )HPLD * 3HWURQH * 6SDJQXROR DQG 0 9LWHOOL ³2SWL PL]DWLRQ RI SHUWXUE DQG REVHUYH PD[LPXP SRZHU SRLQW WUDFNLQJ PHWKRG´ ,((( 7UDQVDFWLRQV RQ 3RZHU (OHFWURQLFV YRO QR SS ± -XO\
>@ % 6XEXGKL DQG 5 3UDGKDQ ³$ FRPSDUDWLYH VWXG\ RQ PD[LPXP SRZHU SRLQW WUDFNLQJ WHFKQLTXHV IRU SKRWRYROWDLF SRZHU V\V WHPV´,((( 7UDQVDFWLRQV RQ 6XVWDLQDEOH (QHUJ\ YRO QR SS ± -DQ
>@ 0 $ * GH %ULWR / *DORWWR / 3 6DPSDLR * G $ H 0HOR DQG & $ &DQHVLQ ³(YDOXDWLRQ RI WKH PDLQ PSSW WHFKQLTXHV IRU SKRWRYROWDLF DSSOLFDWLRQV´,((( 7UDQVDFWLRQV RQ ,QGXVWULDO (OHFWURQLFV YRO QR SS ± 0DUFK
>@ ( ' $UDQGD - $ * *DODQ 0 6 GH &DUGRQD DQG - 0 $ 0DUTXH] ³0HDVXULQJ WKH LY FXUYH RI SY JHQHUDWRUV´ ,(((
,QGXVWULDO (OHFWURQLFV 0DJD]LQH YRO QR SS ± 6HSW
>@ 0 .LOOL DQG 6 6DPDQWD ³0RGL¿HG SHUWXUE DQG REVHUYH PSSW DOJRULWKP IRU GULIW DYRLGDQFH LQ SKRWRYROWDLF V\VWHPV´ ,(((
7UDQVDFWLRQV RQ ,QGXVWULDO (OHFWURQLFV YRO QR SS ± 6HSW
>@ : ;LDR 0 6 ( 0RXUVL 2 .KDQ DQG ' ,Q¿HOG ³5HYLHZ RI JULGWLHG FRQYHUWHU WRSRORJLHV XVHG LQ SKRWRYROWDLF V\VWHPV´
,(7 5HQHZDEOH 3RZHU *HQHUDWLRQ YRO QR SS ±
>@ 3 0 *DUFLD9LWH $ 6RULDQR5DQJHO - & 5RVDV&DUR DQG ) 0DQFLOOD'DYLG ³$ GFGF FRQYHUWHU ZLWK TXDGUDWLF JDLQ DQG LQSXW FXUUHQW ULSSOH FDQFHODWLRQ DW D VHOHFWDEOH GXW\ F\FOH´
5HQHZDEOH (QHUJ\ YRO SS ± >2QOLQH@
$YDLODEOH KWWSZZZVFLHQFHGLUHFWFRPVFLHQFHDUWLFOH
>@ 1 0RKDQ 7 0 8QGHODQG DQG : 3 5REELQV 3RZHU (OHF WURQLFV &RQYHUWHUV $SSOLFDWLRQV DQG 'HVLJQ UG HG -RKQ :LOH\ DQG 6RQV ,QF
>@ $ 3 %KDWQDJDU DQG % 5 . 1HPD ³&RQYHQWLRQDO DQG JOREDO PD[LPXP SRZHU SRLQW WUDFNLQJ WHFKQLTXHV LQ SKRWRYROWDLF DS SOLFDWLRQV $ UHYLHZ´ -RXUQDO RI 5HQHZDEOH DQG 6XVWDLQDEOH (QHUJ\ YRO QR S 0D\
>@ % $[HOURG < %HUNRYLFK $ 6KHQNPDQ DQG * *RODQ ³'LRGH FDSDFLWRU YROWDJH PXOWLSOLHUV FRPELQHG ZLWK ERRVWFRQYHUWHUV WRSRORJLHV DQG FKDUDFWHULVWLFV´ ,(7 3RZHU (OHFWURQLFV YRO QR SS ± -XO\
>@ & & +XD < + )DQJ DQG : 7 &KHQ ³+\EULG PD[LPXP SRZHU SRLQW WUDFNLQJ PHWKRG ZLWK YDULDEOH VWHS VL]H IRU SKR WRYROWDLF V\VWHPV´,(7 5HQHZDEOH 3RZHU *HQHUDWLRQ YRO QR SS ±
>@ + $ 6KHU $ ) 0XUWD]D $ 1RPDQ . ( $GGRZHHVK . $O +DGGDG DQG 0 &KLDEHUJH ³$ QHZ VHQVRUOHVV K\EULG PSSW DOJRULWKP EDVHG RQ IUDFWLRQDO VKRUWFLUFXLW FXUUHQW PHDVXUHPHQW DQG S R PSSW´ ,((( 7UDQVDFWLRQV RQ 6XVWDLQDEOH (QHUJ\
YRO QR SS ± 2FW
>@ / 0 (OREDLG $ . $EGHOVDODP DQG ( ( =DN]RXN ³$UWL¿FLDO QHXUDO QHWZRUNEDVHG SKRWRYROWDLF PD[LPXP SRZHU SRLQW WUDFN LQJ WHFKQLTXHV D VXUYH\´ ,(7 5HQHZDEOH 3RZHU *HQHUDWLRQ YRO QR SS ±
>@ ' 1 0 9LODWKJDPXZD DQG 6 *DPLQL3RZHU (OHFWURQLFV IRU 3KRWRYROWDLF 3RZHU 6\VWHPV 0RUJDQ &OD\SRRO
>@ ( .RXWURXOLV DQG . .DODLW]DNLV ³1RYHO EDWWHU\ FKDUJLQJ UHJX ODWLRQ V\VWHP IRU SKRWRYROWDLF DSSOLFDWLRQV´,(( 3URFHHGLQJV (OHFWULF 3RZHU $SSOLFDWLRQV YRO QR SS ± 0DU
>@ 0 .LOOL DQG 6 6DPDQWD ³$Q DGDSWLYH YROWDJHVHQVRUEDVHG PSSW IRU SKRWRYROWDLF V\VWHPV ZLWK VHSLF FRQYHUWHU LQFOXGLQJ VWHDG\VWDWH DQG GULIW DQDO\VLV´,((( 7UDQVDFWLRQV RQ ,QGXVWULDO (OHFWURQLFV YRO QR SS ± 'HF
>@ ) = 3HQJ ³= VRXUFH LQYHUWHU´,((( 7UDQVDFWLRQV RQ ,QGXVWU\
$SSOLFDWLRQV YRO QR S 0DU
>@ 6RODUH[6RODUH[ 06; 0DQXIDFWXUHU 6SHFL¿FDWLRQ VKHHW 6R ODUH[ )UHGHULFN 0' 86$
>@ 6 3XNKUHP ³$ SKRWRYROWDLF SDQHO PRGHO LQ PDWODEVLPXOLQN´
WK VWXGHQWV¶ VFLHQFH FRQIHUHQFH %HGOHZR SS ± 2FW
